Stochastic linear systems subject to time-varying parameter uncertainties affecting both system dynamics and noise statistics are considered. A linear filter is used to estimate a linear combination of the states of the system. When the filter is given, the stabilizing solution of a suitable Riccati equation is shown to yield an upper bound for the covariance of the estimator error. The main problem addressed in the paper is the design of an ’optimal robust filter’ that minimizes such a covariance bound. Necessary conditions are given for the existence of an optimal reduced-order robust filter as well as necessary and sufficient conditions for the full-order case. The computation of the optimal filter calls for the solution of a Riccati equation that generalizes the standard Riccati equation for the Kalman filtering problem. A numerical example is provided in which the new filter is compared with both the Kalman and H-infinity-filters.